If you want to run fixed, yes. A track wheel has two opposing threads on it. The cog threads on with right hand threads and then a lockring on top of that using left hand threads. This way, if the cog starts to loosen while the rider pushes back on the pedals, it will tighten the lockring and keep the cog from falling off.

The wheel on that bike just has one set of threads. Because there is a freewheel, there is never any reverse torque to unscrew it. You could run a single speed freewheel on the bike safely.

Unfortunately, those chainrings look riveted on. It's not uncommon on older entry level bikes. It also means you can't really change the chainrings.

So, absolute cheapest option is to have a 3/32 singlespeed freewheel installed on the back and put on a 3/32 chain. Just use the existing chainrings and ignore that there's an extra one... it's a bit weird but it gets you to a singlespeed.

To get to fixed gear you will need a new rear wheel. You might look around on CL or FB marketplace and see if someone is selling one. The other issue here is that your bike will likely have 27" rims. Anything modern will use 700c rims that are about 4mm smaller in radius. If your brake calipers have room to move the pads down then that's fine. If not... new calipers also. Used calipers off Ebay can be quite affordable

TBH, none of this is hard to do, unless it's all new to you... are there any local bike clubs near you? I'm kinda across the state, south of Flint...